Definoval

Definoval is a theoretical construct used in discussions of definitional systems and semantics. It denotes a self-contained unit that groups a finite set of primitive terms with a single evaluative predicate that determines the truth of statements defined within that unit. A definoval is designed to be closed under its internal inference rules, so that any statement expressible within the unit can be evaluated without reference to external definitions.

Origin and naming: The term "definoval" was coined in a 2020s thought experiment by linguist and logician A. Doe to illustrate how definitions can be localized into compact, circular-free blocks. It combines "define" with "oval" to suggest a contained, curved boundary around definitions.

Formal properties: A definoval D consists of a finite set P of primitive symbols, a set R of inference rules, and a valuation function v that assigns truth values to statements built from P using R. D is closed if every statement built from P using R is decidable by v without appealing to outside definitions. Definovals can coexist by mapping relations between them.

Example: Consider a definoval with primitive terms {A, B} and a rule that A is true if B is true, and B is true if A is true. The unique fixpoints are A and B true together or both false, illustrating how circularities yield a bounded truth space within the unit.

See also: fixed point, circular definition, semantic networks, formal semantics. Note: Definoval is a fictional concept used for illustrative purposes in this article.